I'll do some coloring:

12r+4s-6r-6s=?


The two red terms are like terms because they have the same letter r.
They don't have the same coefficient, but they have the same letter,
so they are considered like terms and they can be combined.

The two blue terms are like terms because they have the same letter s. 
They also don't have the same coefficient, but they have the same letter, 
so they are considered like terms and they can be combined.

To keep things straight, sometimes people rearrange the terms first
so that they will be together, like this, where I have swapped the middle
two terms:

12r-6r+4s-6s?

Then to combine the two red terms, we just combine their coefficients
12-6 getting 6 and then put on the r, getting 6r.

To combine the two blue terms, we similarly combine their coefficients 
+4-6 getting -2 and then put on the s, getting -2s.

So the final answer is 6r-2s

Edwin